In quantum mechanics, the conservation of information and the reversibility of physical processes are fundamental concepts. These concepts stem from the underlying principles of quantum mechanics and are not explicitly postulated as axioms. Let's explore why this is the case.
One of the key principles in quantum mechanics is unitarity, which states that the total probability of all possible outcomes in a quantum system must always sum to 1. In other words, the evolution of a quantum system is governed by unitary transformations, which are reversible. This reversibility ensures that information is conserved and that no information is lost during the evolution of a closed quantum system.
The Schrödinger equation, the fundamental equation of quantum mechanics, describes the time evolution of quantum states. It is a unitary equation, meaning that the evolution it describes is reversible. This implies that if you know the quantum state of a system at one time, you can theoretically determine its past and future states.
Another important concept related to reversibility is time symmetry. In quantum mechanics, the laws of physics are time-symmetric, which means that the equations that govern the evolution of a system are the same whether time progresses forward or backward. While macroscopic phenomena often exhibit time asymmetry (such as objects breaking or dissolving over time), these phenomena can be understood as arising from statistical considerations at the microscopic quantum level, where the underlying dynamics are time-symmetric.
It is worth noting that while the fundamental laws of quantum mechanics are reversible and conserve information, there are certain processes that may appear irreversible or result in the apparent loss of information when considering only a part of the larger system. For example, when quantum systems interact with their environment, a process called decoherence occurs, which can lead to the loss of coherence and the appearance of irreversible behavior. However, when considering the larger system that includes both the quantum system and its environment, the overall evolution remains reversible, and information is conserved.
In summary, the conservation of information and the reversibility of physical processes in quantum mechanics are inherent properties resulting from the unitarity of quantum evolution and the time symmetry of the underlying laws. These principles are not explicitly postulated but arise naturally from the mathematical framework and fundamental principles of quantum mechanics.